Exact S-matrices for d_{n+1}^{(2)} affine Toda solitons and their bound states

TL;DR

This paper proposes an exact S-matrix for soliton scattering in $d_{n+1}^{(2)}$ affine Toda field theory, constructing bound state amplitudes and validating the conjecture through pole analysis and duality considerations.

Contribution

It introduces a conjectured exact S-matrix based on quantum group R-matrices for $d_{n+1}^{(2)}$ affine Toda solitons, including bound states, with validation via pole structure analysis.

Findings

S-matrix conjecture matches pole structure expectations

Breather-particle identification confirmed for lowest breathers

Implications for duality in affine Toda theories discussed

Abstract

We conjecture an exact S-matrix for the scattering of solitons in $d_{n+1}^{(2)}$ affine Toda field theory in terms of the R-matrix of the quantum group $U_q(c_n^{(1)})$. From this we construct the scattering amplitudes for all scalar bound states (breathers) of the theory. This S-matrix conjecture is justified by detailed examination of its pole structure. We show that a breather-particle identification holds by comparing the S-matrix elements for the lowest breathers with the S-matrix for the quantum particles in real affine Toda field theory, and discuss the implications for various forms of duality.